DFT study of superhalogen and superalkali doped graphitic carbon nitride and its non-linear optical properties

Abstract

DFT calculations are carried out to investigate nonlinear optical (NLO) properties of superhalogen (BCl₄) and superalkali (NLi₄) doped graphitic carbon nitride (GCN). It is noted that the geometries of doped GCN are sufficiently stable. The energy gap for GCN is 3.89 and it reduces to 0.53 eV in our designed molecule G4. Change in the dipole and transition dipole moment is observed along with small transition energies which are responsible for higher hyperpolarizabilities. Doped GCN has larger first and second hyperpolarizabilities which are basic requirements for NLO response. The second hyperpolarizability of GCN enhances from 1.59 × 10⁴ to 2.53 × 10⁸ au when doping with BCl₄ and NLi₄. TD-DFT calculations show the absorption maxima of doped GCN range from 700 nm to 1350 nm. EDDM analysis provides information on electronic distribution from excited to ground state. All these consequences show doped GCN can be a promising NLO material.

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1. Introduction

Nonlinear optics describes the behavior of light in nonlinear materials and media. While all molecules and materials are nonlinear to some extent, in most cases the optical properties of a substance are not significantly affected by light.^1–4 However, for sufficiently intense light (typically from strong lasers), one can observe nonlinear optical phenomena related to the way intense light alters the optical properties of material systems. Mathematically, nonlinear materials have a response that depends on the strength of the applied field in a nonlinear manner. For example, in conventional or linear optics, the dipole moment per unit volume of a substance (the dielectric polarization) depends on the strength of the applied optical field.^5–9

For the past few decades, nonlinear optical (NLO) materials have earned great attention in the field of photonics because of their vast applications in LASER, LED, optical display, biosensors, scanners and telecommunication and other fields of photonics.^6,10–14 Due to their unique properties of producing new electric and magnetic fields, a large number of NLO materials are produced.^15,16 Two major classes of NLO materials are organic and inorganic NLO materials. Organic NLO materials are more valuable because of their better electronic properties, structural diversity and large NLO coefficient. Inorganic NLO materials also have advantages of their large size, strengths and stability.¹⁷

Several new inorganic and organic materials are synthesized with improved properties. Inorganic phosphides and nitrides, for example, BP, AlP, BN, AlN and GCN¹⁸ can be largely applied in semiconductors, and other electronic and NLO applications.^19–22 There are more efficient materials for many applications and they can be easily synthesized with low cost.²³

Nonlinear optical (NLO) properties of molecules and polymers^24–27 are a subject of high importance in organic chemistry and materials sciences. The theoretical prediction of NLO properties based on quantum chemical calculations is challenging and the development of new, along with improvement of existing, methodology remains a substantial demand for computational chemistry.^28–31 The difficulties that occur in such calculations are related to the fact that the NLO properties render themselves inelastic quantities because they are high-order derivatives of the energy.^32–34 Theoretical investigations have shown that the first hyperpolarizability of inorganic and organic molecules is enhanced by a good approach that is doping of superalkali and superhalogen. Superhalogen comprises electronegative atoms (Cl, F and O) which surrounded the central metal atom. By increasing the electronegative atoms, the added electron is delocalized over the metal atom which increases its electron affinity (EA). The electron affinity of superhalogen goes beyond the electron affinity of the halogen atom. The doping of superalkali leads to the generation of alkalide or electride which increases the value of the first hyperpolarizability. Superalkalis have a lower ionization prospective than alkali metals. The nonlinear response of materials leads to many optical phenomena including changes in the optical properties of the material, generation of new light frequencies, and changes in the phase or the amplitude of the emergent light.^35,36

Liebig reported carbon nitride in 1834 for the first time.³⁷ The GCN has been applied successfully in solar cells, gas and humidity sensors, for the storage of H₂ and CO₂ (ref. 38 and 39) and many others because GCN is thermally stable with a unique electronic framework. In recent years, the NLO response of carbon nanostructures that were sp² hybridized was largely studied.^40,41 In this study, the graphitic carbon nitride cluster (C₁₈N₂₇H₈) was doped with superhalogen (BCl₄) and superalkali (NLi₄). Doping of superhalogen (BCl₄) and superalkali (NLi₄) is an effective way to enhance the NLO response of GCN. Four different complexes of superhalogen (BCl₄) and superalkali (NLi₄) doped GCN were investigated through density functional theory (DFT).^42–44 This study focused on the NLO response, electronic and molecular structure.

2. Computational details

With Gaussian 09 program⁴⁵ all the calculations were performed. Structures of the molecules were drawn through GaussView 5.0.^46,47 6B3LYP method of DFT was used for the geometry optimization and all other calculations with 6-31G (d,p) basis set. 6B3LYP method is quite reliable for geometry optimization and electronic properties of carbon nitride nanosheets.⁴⁸ Energies of HOMO, LUMO and HOMO–LUMO band gap were also computed. The DOS analysis was calculated and plotted by using PyMOlyze software.⁴⁹

The HOMO–LUMO band gap was calculated by eqn (1)

E_H–L = E_L − E_H (1)

Here E_L, E_H and E_H–L are the energies of LUMO, HOMO and HOMO–LUMO.

Vertical Ionization Energies (VIE) were also computed by using the B3LYP method by using eqn (2).

VIE = E(X⁺) − E(X) (2)

Here E(X⁺) and E(X) are the energies of the cation and neutral doped complexes.

B3LYP method was also used to compute values of dipole moment, transition dipole moment, energy of excitation (ΔE), α_iso and α_aniso, first and second hyperpolarizabilities (β_static, γ_static) and oscillator strength (f_o). Energy Difference Diagram Map (EDDM) analysis was also performed using the B3LYP method. TD-DFT method was used for UV/Vis absorption analysis and 20 excited states were studied. With the help of Origin software, the UV/Vis spectra were plotted.

3. Results and discussions

3.1. Geometric parameters

Four different superhalogen (BCL₄) and superalkali (NLi₄) doped complexes were optimized at the B3LYP/6-31G (d,p), level of theory. Pure GCN and doped GCN (G1–G4) were successfully optimized at B3LYP/6-31G(d,p). G1 and G2 contained superhalogen and superalkali on the GCN surface. G3 & G4 contained both superhalogen and superalkali on the same molecule but opposite sides. G3 and G4 contained superhalogen on bowl-inside and superalkali on bowl-outside. G3 and G4 both contain superhalogen on the bowl-in side of GCN, but they differ in the orientation of superalkali on the other side of GCN. In G3, the nitrogen atoms of superalkali are pointing away from the GCN surface whereas, in G4, a lithium atom is present at the end. It was noted that all the doped complexes were satisfactory stable. Carbon–nitrogen bond lengths (C=N) were computed for pure and all doped complexes. It was examined that, for pure GCN, carbon–nitrogen bonds (C=N) were 1.32 Å. C=N bond lengths were increased from 1.32 Å for pure GCN to 1.34, 1.35, 1.38 Å for G1, G3 & G4, respectively. On the other hand, the C=N bond length in G2 was decreased to 1.30 Å. Front and side views (a and b respectively) of optimized geometries for pure GCN and doped G1–G4 complexes are shown in Fig. 1.

Fig. 1 Optimized geometries of pure GCN and G1–G4.

Reported DFT calculations for band gap for different forms of C₃N₄ are listed in Table 1. The band gap of α-C₃N₄, β-C₃N₄, cubic-C₃N₄, pseudocubic C₃N₄, g-h-triazine, g-o-triazine and g-h-heptazine is 5.49 eV, 4.85 eV, 4.30 eV, 4.13 eV, 2.97 eV, 0.93 eV and 2.88 eV, respectively.⁵⁰ Two major types of g-C₃N₄ are s-triazine and tri-s-triazine that are linked with tertiary amine groups. Tri-s-triazine is more stable and showed excellent structural, nonlinear optical and physiological properties. The band gap for our proposed form of g-C₃N₄ (tri-s-triazine) is 3.89 eV. Literature study show that our selected model of g-C₃N₄ is a highly stable isomeric form among the other reported forms of g-C₃N₄.⁵⁰

Table 1 The band gap of α-C₃N₄, β-C₃N₄, cubic-C₃N₄, pseudocubic C₃N₄, g-h-triazine, g-o-triazine and g-h-heptazine.⁵⁰

Molecule	Band gap eV
α-C3N4	5.49
β-C3N4	4.85
Cubic-C3N4	4.3
Pseudocubic C3N4	4.13
g-h-triazine	2.97
g-o-triazine	0.97
g-h-heptazine	2.88

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For understanding the electrical and optical properties of the pure GCN and all the designed G1–G4 molecules, energies of HOMO, LUMO and their H–L gaps were calculated. HOMO is electron-rich and represents the donating ability of the molecule. Whereas LUMO illustrates the electron-withdrawing ability. The FMOs (Frontier Molecular Orbitals) of pure GCN and designed molecules (G1–G4) using B3LYP/6-31G (d,p) are shown in Fig. 2. The E_HOMO of pure GCN and G1, G2, G3 and G4 are −6.10, −6.37, −3.14, −3.57 and −3.59 eV, respectively, while the E_LUMO of pure GCN and G1, G2, G3 and G4 are −2.22, −2.65, −2.38, −2.78 and −2.61 eV respectively given in Table 2. Doping of BCl₄ and NLi₄ on GCN reduces its energy as new energy levels are generated among these molecules that narrow the energy difference. The energy gap (E_g) for pure GCN and G1, G2, G3 and G4 are 3.89, 3.72, 0.75, 0.79 and 0.98 eV, respectively. This reduction of the energy gap enhances its electronic conduction and makes it easy for electrons to excite from HOMO to LUMO. The decreasing order of E_g is pure GCN > G1 > G4 > G3 > G2. HOMO and LUMO energy gap of G1–G4 are low as compared with pure GCN. The G1 molecule has the highest energy gap of 3.72 eV (Fig. 3).

Fig. 2 HOMO LUMO for pure GCN and G1–G4.

Table 2 Energies of HOMO, LUMO for pure GCN and G1–G4

Molecule	HOMO (eV)	LUMO (eV)
Pure GCN	−6.1	−2.22
G1	−6.37	−2.65
G2	−3.14	−2.38
G3	−3.57	−2.78
G4	−3.59	−2.61

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Fig. 3 Energy band gaps for pure GCN and G1–G4 complexes.

Vertical ionization energies for all doped complexes were also computed and their values are 6.10, 6.37, 3.14, 3.57 and 3.59 eV of pure GCN and G1, G2, G3 and G4, respectively. The decreasing order for VIE of all pure and doped complexes is pure GCN > G1 > G4 > G3 > G2. All the values are given in Table 3.

Table 3 Energy gaps and vertical ionization energies for pure GCN and G1–G4

Molecule		Eg (eV)	VIE (eV)
Pure GCN		3.89	6.1
G1		3.72	6.37
G2	0.75	3.14
G3	0.79	3.57
G4	0.98	3.59

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For the understanding of the HOMO–LUMO gap reduction, the density of states (DOS) analysis was performed at the same level of theory. DOS plot for pure GCN showed that there is a large gap between HOMO and LUMO. In the analysis of the DOS plot of G1–G4, a reduction of the energy gap was observed for all complexes. In G1, superhalogen donates excess electrons to GCN and because of these electrons, new energy levels are formed which are responsible for the reduction of the energy gap. Superhalogen, without such excess electrons, does not cause any decrease in the H–L gap. All these new energy levels formed between the original HOMOs and LUMOs of pure GCN result in the reduction of the energy gap. PDOS represents the partial DOS analysis of individual superalkali, superhalogen and GCN fragments whereas, TDOS represents the total DOS analysis of doped molecule. In the DOS plots, TDOS for pure GCN (Redlined) in the range of −16 to −5 eV represents occupied states whereas −2 to 9 eV represent virtual states. In the case of G1, PDOS of pure GCN and TDOS of doped GCN (indicated by red and green lines) ranging from −16 to −5 eV represent HOMO and from −2 to 9 eV represent LUMO but the doped GCN exhibit sharp green peaks in its TDOS representation which is ascribed for the dominant effect of doping in reducing energy gap. In the DOS plot of G2, PDOS of individual superalkali (NLi₄), superhalogen (BCl₄) and GCN (indicated by black Red and green lines) and TDOS of doped GCN (indicated by the blue line), ranging from −13 to −5 eV represent HOMO and from −4 to 9 eV represent LUMO and LUMO+2. The sharp blue peaks indicate the greater contribution of electron density from doped GCN as well as the higher HOMO and lower LUMO energy levels of G2 become the cause for reduction of the energy gap. In the DOS plot of G3, PDOS of superalkali (NLi₄) and pure GCN and TDOS of doped GCN (indicated by black, red and green lines respectively) ranging from −14 to −4 eV represent HOMO and HOMO-2 and from −5 to 9 eV represent LUMO and LUMO+1. The flat red peak of pure GCN in the HOMO region shows its little electronic contribution but the sharp green peaks of doped GCN plausibly explain the high electronic contribution due to the strong effect of dopant in reducing the energy gap. Similar is the case with G4. DOS plots for pure GCN and G1–G4 are shown in Fig. 4.

Fig. 4 DOS plots for pure GCN and G1–G4 complexes.

To understand the nature of excitation, orbital transitions analysis was performed for pure and doped complexes. For pure GCN and G1, the transition took place from HOMO to LUMO, whereas in G2, the transition took place from HOMO to LUMO+2. For G3 transition took place from HOMO-2 to LUMO+1 whereas it is from HOMO-1 to LUMO+1 in G4. These new energy levels which were formed between the original HOMO and LUMO are the evidence of reduction of the energy gap. All these transitions are graphically represented in Fig. 5.

Fig. 5 Transition diagrams pure GCN and G1–G4 complexes.

3.2. Non-linear optical properties

The dipole moments for pure GCN and G1–G4 were computed and it was noted that the dipole moment was changed on doping superhalogen and superalkali on GCN. For pure GCN, it is 1.81 D whereas dipole moments are 5.24, 4.14, 4.84 and 8.33 D for G1, G2, G3 and G4, respectively. The increasing order of dipole moment is pure GCN < G2 < G3 < G1 < G4. Pure GCN has a low dipole moment due to the symmetry and this symmetry is broken when a dopant is introduced on GCN. Among the doped structures, G1 and G2 are singly doped either containing superalkali or a super halogen whereas G3 and G4 contain both superakali and superhalogen on the opposite faces of the GCN sheet. In G3 and G4, the superalkali serves as a source of electrons whereas superhalogen is the acceptor moiety. A deep analysis reveals that the dipole moments are higher for systems containing superhalogen and the dipole moment vector in these complexes starts from the halogen of BCl₄ and ends up towards the GCN surface. G3 and G4 both contain superhalogen on the bowl-in side of GCN, but they differ in the orientation of superalkali on the other side of GCN. In G3, the nitrogen atoms of superalkali are pointing away from the GCN surface whereas, in G4, a lithium atom is present at the end. The presence of a lithium atom at the end in G4 creates a positive pole whereas a halogen of BCl₄ (on the other end) creates a negative pole. The presence of clear positive and negative poles with a large distance between them leads to a larger dipole moment of G4 over G3. Moreover, the dipole moment vector of G4 is not on the axis connecting the superalkali with superhalogen rather it is tilted on the side which leads to a lower dipole moment.

The transition dipole moment for pure GCN and G1–G4 was also computed and it was noted that the transition dipole moments were changed on doping superhalogen and superalkali on GCN. For G1–G4, these are 0.0192, 0.1235, 0.0237 and 0.0052 D respectively. The increasing order of transition dipole moment is G4 < G1 < G3 < G2. The values of dipole moment transition dipole moment for pure GCN and G1–G4 are listed in Table 4.

Table 4 Dipole moment transition dipole moment for pure GCN and G1–G4

Molecule	μ (D)	Δμ (D)
Pure GCN	1.81
G1	5.24	0.0192
G2	4.14	0.1235
G3	4.84	0.0237
G4	8.33	0.0052

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For all complexes linear isotropic and anisotropic polarizabilities (α_iso and α_aniso) were computed. For pure GCN α_iso is 437.54 au and it increased on doping to 932.39, 745.64, 723.89 and 656.01 for G1, G2, G3 and G4, respectively, respectively. Values of α_iso increase in order pure GCN < G4 < G3 < G2 < G1. α_aniso of pure GCN is 438.89 au and it changed on doping to 659.13, 512.73, 453.29 and 198.63 au for G1, G2, G3 and G4, respectively. α_aniso increase in the order G4 < pure GCN < G3 < G2 < G1. Values for all complexes linear isotropic and anisotropic are listed in Table 5.

Table 5 Linear isotropic and anisotropic for pure GCN and G1–G4

Molecule	αiso (au)	αaniso (au)
Pure GCN	437.54	438.89
G1	932.39	659.13
G2	745.64	512.73
G3	723.89	453.29
G4	656.01	198.63

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For the NLO response, hyperpolarizability is the major property. First and second hyperpolarizabilities (β_static and γ_static) were also computed. β_static for pure GCN is 95.37 au and β_static values are 74 703, 90 733, 23 325 and 25 738 au for G1, G2, G3 and G4, respectively. β_static increased in the order: pure GCN < G3 < G4 < G1 < G2. γ static for pure GCN is 1.59 × 10⁴ and values for G1–G4 are 2.07 × 10⁸, 2.53 × 10⁸, 1.14 × 10⁶ and 4.43 × 10⁵ au respectively. Values of γ_static increase in order pure GCN < G4 < G3 < G2 < G1. Dipole moment (μ in D), α_iso and α_aniso in au, β_static in au and γ_static in au are graphically represented in Fig. 6, Fig. 7, Fig. 8 and Fig. 9, respectively. A two-level approximation is a frequently used model that supports the calculation of nonlinearities especially the first hyperpolarizability as follows.⁵¹

where Δμ, f_o and ΔE³ are the transition dipole moment from the ground to the excited state, highest oscillator strength and transition energy for the crucial excitations, respectively. The small values for ΔE of G1–G4 show that these complexes have larger hyperpolarizabilities. f_o for pure GCN is zero and it was changed for G1–G4. The values of f_o are 0.0001, 0.0006, 0.0054 and 0.0035 for G1–G4, respectively. Hyperpolarizabilities for all complexes are given in Table 6.

Fig. 6 Dipole moment (μ) for pure GCN and G1–G4.

Fig. 7 First hyperpolarizability (β_static) for pure GCN and G1–G4.

Fig. 8 Linear isotropic (α_iso) and anisotropic (α_aniso) polarizabilities for pure and G1–G4.

Fig. 9 Second hyperpolarizability for pure GCN and G1–G4.

Table 6 First and second hyperpolarizabilities (β_static, γ_static) for all complexes

Molecule	βstatic (au)	γstatic (au)
Pure GCN	95.37	1.59 × 10^4
G1	74 703	2.07 × 10^8
G2	90 733	2.53 × 10^8
G3	23 325	1.14 × 10^6
G4	25 738	4.43 × 10^5

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Excitation energy (ΔE) and oscillator strength (f_o) for G1–G4 are given in Table 7.

Table 7 Oscillator strength (f_o) and transition orbital for G1–G4

Molecule	fo	ΔE eV
G1	0.0001	0.0283
G2	0.0006	0.2378
G3	0.0054	0.1068
G4	0.0035	0.422

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Absorption energies of pure GCN and G1–G4 are computed through time-dependent DFT (TD-DFT). 20 excited states were studied, and it was noted that pure GCN absorbs at 350 nm. After doping superhalogen and superalkali absorption maxima are red-shifted. All the doped structures absorb radiations in the visible and IR region. The λ_max for G1, G2, G3 and G4 are 780, 1350, 1290 and 1045 nm. This shows that these doped complexes have valuable absorption for NLO response. Absorption spectra for pure GCN and G1–G4 are shown in Fig. 10. Absorption (λ_max) and transition orbital for G1–G4 are listed in Table 8.

Fig. 10 UV-vis spectra for pure GCN and G1–G4.

Table 8 Absorption (λ_max) and transition orbital for G1–G4

Molecule	λmax (nm)	% C.I transition
G1	780	97% H → L
G2	1350	96% H → L+2
G3	1290	84% H-2 → L+1
G4	1045	50% H-1 → L+1

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3.3. EDDM analysis

Electron Density Difference Map (EDDM) analysis of pure GCN and G1–G4 complexes was carried out at the B3LYP/6-31G level of theory. For a better understanding of resultant charge density over the molecule, EDDM analysis was carried out. Images of EDDM gave information about the electronic distribution of pure GCN and doped complexes G1–G4 from excited to ground state transition (ρ_excited − ρ_ground). Two different colors were seen in EDDM images (sea-green and purple color). The reduced density of electrons shown in purple color with a negative value and electron reorganizations with a positive value with sea-green color represents the electronic density growth. EDDM images for pure GCN and doped G1–G4 are shown in Fig. 11.

Fig. 11 EDDM of pure GCN and G1–G4.

4. Conclusions

NLO response of superhalogen (BCL₄) and superalkali (NLi₄) doped graphitic carbon nitride (GCN) was investigated by density field theory (DFT) methods. It was noted that all the doped complexes (G1–G4) were geometrically stable. Reduction of HOMO–LUMO energy gap was noted for all G1–G4. For pure GCN, the energy gap is 3.89 eV. G1 showed the highest energy gap of 3.72 eV among doped clusters. VIEs for all G1–G4 were changed for all G1–G4. The increase in dipole moment was observed for G1–G4. It was also observed that the values of ΔE were small which indicates higher values of hyperpolarizabilities. Doping of superhalogen and superalkali on GCN change linear isotropic and anisotropic polarizabilities which are responsible for their NLO response. Moreover, the first and second hyperpolarizability (β_static and γ_static) were changed. β_static for pure GCN was 95.37 au and for G3 it was increased to 90 733 au. All these changes after doping enhanced the NLO response of GCN. All the doped complexes show absorption in the range of 700 to 1350 nm. All the results propose that superhalogen and superalkali co-doped graphitic carbon nitride (G1–G4) can be promising candidates as NLO material.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors acknowledge the financial and technical support from the Punjab Bio-energy Institute (PBI) and the University of Agriculture Faisalabad (UAF).

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